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University of North Texas

1. Cotton, Michael R. Abelian Group Actions and Hypersmooth Equivalence Relations.

Degree: 2019, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc1505289/

We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.
*Advisors/Committee Members: Gao, Su, Jackson, Stephen C., Kallman, Robert R..*

Subjects/Keywords: abelian; group action; hypersmooth; equivalence relation; Borel; hyperfinite; essentially hyperfinite; locally compact; LCA-group

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APA (6^{th} Edition):

Cotton, M. R. (2019). Abelian Group Actions and Hypersmooth Equivalence Relations. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc1505289/

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Cotton, Michael R. “Abelian Group Actions and Hypersmooth Equivalence Relations.” 2019. Thesis, University of North Texas. Accessed September 26, 2020. https://digital.library.unt.edu/ark:/67531/metadc1505289/.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Cotton, Michael R. “Abelian Group Actions and Hypersmooth Equivalence Relations.” 2019. Web. 26 Sep 2020.

Vancouver:

Cotton MR. Abelian Group Actions and Hypersmooth Equivalence Relations. [Internet] [Thesis]. University of North Texas; 2019. [cited 2020 Sep 26]. Available from: https://digital.library.unt.edu/ark:/67531/metadc1505289/.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cotton MR. Abelian Group Actions and Hypersmooth Equivalence Relations. [Thesis]. University of North Texas; 2019. Available from: https://digital.library.unt.edu/ark:/67531/metadc1505289/

Not specified: Masters Thesis or Doctoral Dissertation

Texas A&M University

2.
Redelmeier, Daniel.
The Amalgamated Free Product of *Hyperfinite* von Neumann Algebras.

Degree: PhD, Mathematics, 2012, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11058

We examine the amalgamated free product of hyperfinite von Neumann algebras. First we describe the amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras. In this case the result is always the direct sum of a hyperfinite von Neumann algebra and a finite number of interpolated free group factors. We then show that this class is closed under this type of amalgamated free product. After that we allow amalgamation over possibly infinite dimensional multimatrix subalgebras. In this case the product of two hyperfinite von Neumann algebras is the direct sum of a hyperfinite von Neumann algebra and a countable direct sum of interpolated free group factors. As before, we show that this class is closed under amalgamated free products over multimatrix algebras.
*Advisors/Committee Members: Dykema, Ken (advisor), Anshelavich, Michael (committee member), Smith, Roger (committee member), Dahm, Fred (committee member).*

Subjects/Keywords: amalgamated free product; hyperfinite; von Neumann algebra; interpolated free group factor

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Redelmeier, D. (2012). The Amalgamated Free Product of Hyperfinite von Neumann Algebras. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11058

Chicago Manual of Style (16^{th} Edition):

Redelmeier, Daniel. “The Amalgamated Free Product of Hyperfinite von Neumann Algebras.” 2012. Doctoral Dissertation, Texas A&M University. Accessed September 26, 2020. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11058.

MLA Handbook (7^{th} Edition):

Redelmeier, Daniel. “The Amalgamated Free Product of Hyperfinite von Neumann Algebras.” 2012. Web. 26 Sep 2020.

Vancouver:

Redelmeier D. The Amalgamated Free Product of Hyperfinite von Neumann Algebras. [Internet] [Doctoral dissertation]. Texas A&M University; 2012. [cited 2020 Sep 26]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11058.

Council of Science Editors:

Redelmeier D. The Amalgamated Free Product of Hyperfinite von Neumann Algebras. [Doctoral Dissertation]. Texas A&M University; 2012. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11058

3. Iushchenko, Kateryna. On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w.

Degree: PhD, Mathematics, 2012, Texas A&M University

URL: http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10355

This dissertation is devoted to several questions that arise in operator algebra theory. In the first part of the work we study the dilations of homomorphisms of subalgebras to the algebras that contain them. We consider the question whether a contractive homomorphism of a logmodular algebra into B(H) is completely contractive, where B(H) denotes the algebra of all bounded operators on a Hilbert space H. We show that every logmodular subalgebra of Mn(C) is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured by V. Paulsen and M. Raghupathi. In particular, this shows that every unital contractive representation of a logmodular subalgebra of Mn(C) is automatically completely contractive.
In the second part of the dissertation we investigate certain matrices composed of mixed, second?order moments of unitaries. The unitaries are taken from C??algebras with moments taken with respect to traces, or, alternatively, from matrix algebras with the usual trace. These sets are of interest in light of a theorem of E. Kirchberg about Connes' embedding problem and provide a new approach to it.
Finally, we give a modification of I. Klep and M. Schweighofer?s algebraic reformulation of Connes' embedding problem by considering the ?-algebra of the countably generated free group. This allows us to consider only quadratic polynomials in unitary generators instead of arbitrary polynomials in self-adjoint generators.
*Advisors/Committee Members: Pisier, Gilles (advisor), Dykema, Kenneth (committee member), Smith, Roger (committee member), Dahm, Frederik (committee member).*

Subjects/Keywords: logmodular algebras; similarity; connes embedding; hyperfinite

…simple example of finite von Neumann algebra is the *hyperfinite* II1 factor, denoted by R, which… …embeds in
the ultrapower Rω of the *hyperfinite* II1 –factor R. This is well known to be… …x29; \ N be a free ultrafilter on N and R be the *hyperfinite* II1 -factor
with faithful…

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Iushchenko, K. (2012). On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10355

Chicago Manual of Style (16^{th} Edition):

Iushchenko, Kateryna. “On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w.” 2012. Doctoral Dissertation, Texas A&M University. Accessed September 26, 2020. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10355.

MLA Handbook (7^{th} Edition):

Iushchenko, Kateryna. “On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w.” 2012. Web. 26 Sep 2020.

Vancouver:

Iushchenko K. On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w. [Internet] [Doctoral dissertation]. Texas A&M University; 2012. [cited 2020 Sep 26]. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10355.

Council of Science Editors:

Iushchenko K. On Two Properties of Operator Algebras: Logmodularity of Subalgebras, Embeddability into R^w. [Doctoral Dissertation]. Texas A&M University; 2012. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10355